Are cloth simulations affected by scene units?
Yes - size will significantly affect all of the physics simulations. Of particular interest will be the acceleration due to gravity; by having a 10x too large scene you are effectively applying only 1/10th of the force of gravity (which could explain the tissue-paper behaviour of your cloth).
Quick solution would be to adjust the scene gravity by a suitable factor to account for your increased scale (eg, change from -9.8m/s to -98m/s for a 10x change in scale). However, you might still get it behaving a bit oddly since any stiffness and weight will be similarly affected by the scale.